1. Field of the Invention
The present invention relates to a method of determining the rate of penetration (ROP) of a drill bit from measurements made at the surface while drilling from a floating rig.
2. Description of the Related Art
In the rotary drilling of wells such as hydrocarbon wells, a drill bit is located at the end of a drill string formed from a number of hollow drill pipes attached end to end which is rotated so as to cause the bit to drill into the formation under the applied weight of the drill string. The drill string is suspended from a hook and as the bit penetrates the formation, the hook is lowered so as to allow the drill string to descend further into the well. The ROP has been found to be a useful parameter for measuring the drilling operation and provides information about the formation being drilled and the state of the bit being used. Traditionally, ROP has been measured by monitoring the rate at which the drill string is lowered into the well at the surface. However, as the drill string, which is formed of steel pipes, is relatively long the elasticity or compliance of the string can mean that the actual ROP of the bit is considerably different to the rate at which the string is lowered into the hole. The errors which can be caused by this effect become progressively larger as the well becomes deeper and the string longer, especially if the well is deviated when increased friction between the string and the borehole wall can be encountered.
Certain techniques have been proposed to overcome these potential problems. In U.S. Pat. No. 2,688,871 and U.S. Pat. No. 3,777,560 the drill string is considered as a spring and the elasticity of the string is calculated theoretically from the length of the drill string and the Young's modulus of the pipe used to form the string. This information is then used to calculate ROP from the load applied at the hook suspending the drill string and the rate at which the string is lowered into the well. These methods suffer from the problem that no account is taken of the friction encountered by the drill string as a result of contact with the wall of the well. FR 2038700 proposes a method to overcome this problem in which the modulus of elasticity is measured in situ. This is achieved by determining the variations in tension to which the drill string is subjected as the bit goes down the well until it touches the bottom. Since it is difficult to determine exactly when the bit touches the bottom from surface measurements, strain gauges are provided near the bit and a telemetry system is required to relay the information to the surface. This method still does not provide measurements when drilling is taking place and so is inaccurate as well as difficult to implement.
A method is proposed in U.S. Pat. No. 4,843,875 (incorporated herein by reference) in which ROP is measured from surface measurements while drilling is taking place. This method uses the following model: EQU .DELTA.d=.DELTA.s+.LAMBDA..DELTA.h
wherein d is the downhole displacement, s is the surface displacement, .LAMBDA. is the drill string compliance and h is the axial force at the surface. .DELTA. is the difference operator taken over some time interval .tau.. Using the assumptions that over any time interval .tau. (typically 5 minutes) drilling is at an average constant weight on bit (WOB), that the lithology does not change significantly, and the drill string behaves as a perfect spring, then a least squares regression is used to obtain an estimate of .LAMBDA.. In a plot of .DELTA.s against .DELTA.h, .LAMBDA. is the slope of the best fit line through the data points. The derived value of .LAMBDA. can be substituted back into the model to give ROP which can then be integrated to give hole depth. The choice of .tau. and .tau.' may be optimised with field experience. Implementation of this approach means that the drill string compliance is only updated at a time interval of .tau.' and control logic must be incorporated to ensure that the required assumptions are true. If this cannot be done, calculation of compliance must be suspended. PA1 a) determining a displacement .DELTA.s of the drill string at the surface; PA1 b) determining a function of drill string compliance .LAMBDA. from the measurements; PA1 c) determining an axial force .DELTA.T in the suspension system applied at the surface; PA1 d) determining a vertical displacement .DELTA.M of the motion compensator; PA1 e) determining a function of the motion compensator compliance .lambda..sub.M from the measurements; and PA1 f) calculating the bit displacement .DELTA.d from the relationship: ##EQU2## wherein .theta. is a contribution factor of the motion compensator to an axial force applied to the drill string at the surface.
Our co-pending British Patent Application Number 9203844.7 provides a method of determining ROP from surface measurements which can be used where the approach outlined above is undesirable or inappropriate, comprising determining a state space description of the vertical displacement and determining .DELTA.d using Kalman filtering.
When drilling from floating rigs, problems are encountered in the measurement of .DELTA.h which is required for the determination of .DELTA.d in the above described methods. Floating drilling rigs such as drill ships or semi-submersible rigs are subjected to vertical or "heave" motion due to the action of waves on the floating structure. The effect of heave would be to vary the weight applied to the bit by the driller and in extreme circumstances might lift the bit off the bottom of the hole or apply too much weight and cause damage to the bit. In any event, this motion complicates progress of the drilling process. In order to overcome this problem, motion compensators are used in the connection between the drill string and the rig which operate to compensate for the heave motion and allow the weight on bit to be controlled more accurately. However, these compensators do not remove heave effects completely and so there is still potential inaccuracy in the ROP determination.
It is an object of the present invention to provide an improved ROP determination from floating rigs when drilling using a motion compensator. The term "motion compensator" is intended to cover any device interposed between the drill string and the derrick or mast for the purpose of compensating the vertical motion of a floating rig.